A square sheet of metal, that was two metres by two metres, had to be made into an open-topped water tank after four square corners of the sheet were removed. With this information, I had to investigate how the final volume of the tank depended on the size of the squares removed and how the actual size of these squares would produce a tank's volume.
The way I went about this investigation was that I investigated how the size of the squares to be removed created the final volume of the tank. I did this by completing a table, filling out values under the headings: height, length, width and volume. The letter 'h,' (height), was to represent the dimensions in metres of the squares to be removed and these values started from 0 metres and went through to 1. I filled out the rest of the table in a way none other than first subtracting each height value twice, (due to the two sides of the squares), from two giving me a value for length and width because in this case, they are both the same. I then multiplied all three values, (height, length, width), together to get eleven different sets of volumes.
Using the completed table, I then graphed each value of height and volume against each other with height on the horizontal axis and volume on the vertical. I used the scale 2.5cm to represent 0.1m3 for volume and 1.0cm to represent 0.1m for height. Once these points were drawn on and connected, they produced a perfect, smooth curve. This curve then helped me find out that my highest value of 'h,' ('h' represents the dimensions in metres of the square corners to be cut), was a number between 0.3 metres and 0.4 metres, as the curve went higher between the two and it is common knowledge that the higher the line reaches on a graph, in this situation, the bigger the volume is.
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Seeing this, I then took the numbers between 0.3 and 0.4 and calculated, using the same method described earlier, the length, width and volume for each using the numbers 0.
